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Subject: multiple limit cycles ×

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    Andronov-Hopf bifurcation of higher codimensions in a Liènard system
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2011) Schneider, Klaus; Grin, Alexander
    Consider a polynominal Liènard system depending on three parameters itshape a, b, c   and with the following properties: (i) The origin is the unique equilibrium for all parameters. (ii) Ifitshape a crosses zero, then the origin changes its stability, and a limit cycle bifurcates from the euqilibrium. We inverstigate analytically this bifurcation in dependence on the parameters itshape b and itshape c and establish the existence of families of limit cycles of multiplicity one, two and three bifurcating from the origin.